Off axis light beam refraction through a focusing lens system will produce distorted images in a curved plane as opposed to a more desirable flat surface. A flat field scanning lens is a specialized lens system in which the focal plane is a flat surface.
For a typical flat field lens, in the absence of distortion, the beam of light enters the lens at an angle θ compared with the axis of the lens, the position of the spot focused by the lens will be dependent on the product of the focal length (F) of the lens and the tangent of the angle (θ). However, when the lens is designed with built-in barrel distortion, the position of the focused spot can then be made dependent on the product of F and θ, thereby simplifying positioning and image correction algorithms. Lenses designed in this way are called “F-theta” lenses. F-theta lenses are widely used in scanning applications such as laser marking, engraving, and cutting systems.
F-theta lenses are also used for surveillance and reconnaissance applications for precise mapping of an observed target. For these applications, the lens must meet several requirements which do not necessarily apply to other applications. It must provide acceptable images over a wide field of view and must have high resolution and high light sensitivity (i.e. have a low F#). In addition, the lens must be compact, and must provide acceptable images over a wide range of light frequencies, being at least achromatic (able to bring two frequencies to a common focal point) and preferably apochromatic (able to bring three frequencies to a common focal point). In addition, F-theta lenses used for surveillance and reconnaissance should be at least near-telecentric, so that it will produce images that are insensitive to the distance between the lens and the focal plane. If the lens is to be used over a range of temperatures, for example mounted to the exterior of an aircraft, then the lens must be athermal, i.e. invariant over a wide range of temperatures.
U.S. Pat. No. 4,401,362 (Aug. 30, 1983) discloses an F-theta lens for use in optical scanning devices. In such scanning devices the spot from a light beam should move at a constant velocity across the scanning surface. The '362 lens includes three elements and provides a field of view up to 58.2° and an F# of 50. However, the '362 lens would not be suitable for surveillance and reconnaissance applications, since it transmits a very limited amount of light because of its high F# and it has a low resolution. In addition, the '362 lens is suitable only for monochromatic applications, and cannot be used for applications requiring a wide spectrum.
Another example of a prior art F-theta lens is disclosed in U.S. Pat. No. 4,436,383 (Mar. 13, 1984). The '383 lens includes four components and can only be used for monochromatic applications. Its field of view is up to 60.8° and its F# is 19.7. Its resolution is low. For all of these reasons, the '383 lens is only suitable for laser systems applications, and not for surveillance and reconnaissance.
Yet another F-theta lens is disclosed in U.S. Pat. No. 5,835,280 (Nov. 10, 1998). The '280 lens is achromatic having the lateral color compensated electronically, but it is not apochromatic. Its field of view is 54° and its F# is not more than 20. In addition, the '280 lens is too large to be used for reconnaissance and surveillance applications.
Yet another F-theta lens is disclosed in U.S. Pat. No. 6,388,817 (May 14, 2002). The '817 lens is achromatic, has a field of view of 63°, and has an F# of 50. This lens is not apochromatic and its F# is very large, so it cannot be used in low F# reconnaissance and surveillance systems.
The contribution of the optical element to the axial color is the reciprocal of the Abbe number of lens material.
The Abbe number Vd is given byVd=(nd−1)/(nF′−nC′)  (1)where Nd is the index of refraction of the glass at the wavelength of the helium line e (587.6 nm), nF′ is the index of refraction at the blue cadmium line F′ (479.99 nm), and nC′ is the index of refraction at the red cadmium line C′ (643.85 nm).
Accordingly, the smaller the value of Vd, the greater the chromatic dispersion of the glass.
The characterization of optical glass through refractive index and Abbe number alone is not sufficient for high quality optical systems. A more accurate description of the glass properties can be provided by including relative partial dispersions.
The relative partial dispersion Px,y for the wavelengths x and y is defined by the equation:(nx−ny)/(nF−nc)  (2)
The following relationship will approximately apply to the majority of glasses, the so-called “normal glasses”Pxy≈axy+bxyVd  (3)where axy and bxy are specific constants for the given relative partial dispersion Pxy. So as to correct the secondary spectrum and provide an apochromatic lens (i.e. color correction for more than two wavelengths), glasses are required which do not conform to this rule. Therefore glass types having partial dispersions which deviate from Abbe's empirical rule are needed. The ordinate difference ΔP can be used to measure the deviation of the partial dispersion from Abbe's rule. The ordinate difference is given by the following generally valid equation:Pxy=axy+bxy·νd+ΔPxy.  (4)The term ΔPxy therefore quantitatively describes a dispersion behavior that deviates from that of “normal” glasses.
Optical materials expand with rising temperature. The Opto-thermal expansion coefficient β of an optical element is a property of the glass material, and it does not depend on the focal length or shape factor of the individual optics. For a single optical element:β=α+(dn/dT)/(n−1)  (5)                where        α=the thermal expansion coefficient of the glass        n=the refractive index of the glass at the current wave length        T=temperature        
The refractive index of an optical material is also affected by changes in glass temperature. This can be characterized by the temperature coefficient of the refractive index. The temperature coefficient of the refractive index is defined as dn/dt, and varies with wavelength and temperature.
There are two ways of expressing the temperature coefficient of refractive index. One is the absolute coefficient (dn/dt absolute) measured under vacuum, and the other is the relative coefficient (dn/dt relative) measured in ambient air (101.3 kPa {760 torr} dry air).
The absolute temperature coefficient of refractive index (dn/dt absolute) can be calculated using the following formula:dn/dTabsolute=dn/dTrelative+n·dnair/dT  (6)where dnair/dT is the temperature coefficient of refractive index of air listed in the table below.
TABLE ITemperaturednair/dt (10−6/° C.)Range(° C.)tC′He—NeDeF′g−40 to −20−1.34−1.35−1.36−1.36−1.36−1.37−1.38−20 to 0 −1.15−1.16−1.16−1.16−1.16−1.17−1.17 0 to +20−0.99−1.00−1.00−1.00−1.00−1.01−1.01+20 to +40−0.86−0.87−0.87−0.87−0.87−0.88−0.88+40 to +60−0.76−0.77−0.77−0.77−0.77−0.77−0.78+60 to +80−0.67−0.68−0.68−0.68−0.68−0.69−0.69The refractive index of optical glass change with the temperature is given by:
                                          ⅆ                                          n                abs                            ⁡                              (                                  λ                  ,                  T                                )                                                          ⅆ            T                          =                                                            n                2                            ⁡                              (                                  λ                  ,                                      T                    0                                                  )                                                    2              ·                              n                ⁡                                  (                                      λ                    ,                                          T                      0                                                        )                                                              ·                      (                                          D                0                            +                                                2                  ·                                      D                    1                                    ·                  Δ                                ⁢                                                                  ⁢                T                            +                                                3                  ·                                      D                    2                                    ·                  Δ                                ⁢                                                                  ⁢                                  T                  2                                            +                                                                    E                    0                                    +                                                            2                      ·                                              E                        1                                            ·                      Δ                                        ⁢                                                                                  ⁢                    T                                                                                        λ                    2                                    -                                      λ                    TK                    2                                                                        )                                              (        7        )            where                T0: Reference temperature (20° C.)        T: Temperature (° C.)        ΔT: Temperature difference versus T0         λ: Wavelength of the electromagnetic wave in a vacuum (μm)        D0, D1, D2, E0, E1 and λTK: constants depending on glass type.        
The change in the refractive index with temperature usually has the largest impact on the lens performance and thermal focus range.
To make a lens apochromatic a special combination of glasses, Abbe numbers, and partial dispersions is needed. To make a lens athermal, a special combination of glass refractive indices that change with temperature has to be selected. The solution space is dependent on the configuration of the lens, the number of components, and the component shapes.
What is needed, therefore, is a compact F-theta lens having a low F# and a high resolution over a wide field of view, the lens being apochromatic, temperature stable, and near-telecentric over a wide range of light frequencies.